Generally it is not good idea to allow remove already replied post - makes thread flow erratic. Deleting first post (=thread 'root') is even more problematic.
Editing replied post may create problems too, esp when someone decides to delete all content - but then only this post author looks somewhat stupid, not the entire thread :) Thereby I would not block editing.
If and when we get moderators, then it should be possible to report own post with humble request for deletion - then moderator could decide, is post (or in case first post, the entire thread) worth retaining or not.
Another idea would be allow deleting only on test forum - but this requires someone (mod again) to move test posts there.